Geodesic
On passage to the limit in a~multistage multiphase synthesis of substance
Sibirskij žurnal industrialʹnoj matematiki, Tome 15 (2012) no. 4, pp. 135-146

Voir la notice de l'article provenant de la source Math-Net.Ru

We presenta scheme of the proof of passage to the limit to a delayed equation in a model of multistage synthesis of substance when the number of stages increases with the preservation of the time of the whole synthesis when the chain of the synthesis reactions splits into phases. Each phase is characterized by constants defining the intensity of the direct and reverse processes and sinks. It is shown that if the intensity of the direct process dominates the reverse process on each phase with unrestricted number of stages then, when the total number of stages increases, the function that determines the synthesized substance and is defined by the last component of the vector of the solution to the system of ordinary differential equations converges uniformly to the function of the solution to the delayed equation. Numerical estimates of the uniform convergence are obtained for specific values of the parameters.
Keywords: multistage synthesis of substance, passage to the limit, delayed equation. 
@article{SJIM_2012_15_4_a13,
     author = {D. N. Shtokalo},
     title = {On passage to the limit in a~multistage multiphase synthesis of substance},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {135--146},
     publisher = {mathdoc},
     volume = {15},
     number = {4},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2012_15_4_a13/}
}
TY  - JOUR
AU  - D. N. Shtokalo
TI  - On passage to the limit in a~multistage multiphase synthesis of substance
JO  - Sibirskij žurnal industrialʹnoj matematiki
PY  - 2012
SP  - 135
EP  - 146
VL  - 15
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SJIM_2012_15_4_a13/
LA  - ru
ID  - SJIM_2012_15_4_a13
ER  - 
%0 Journal Article
%A D. N. Shtokalo
%T On passage to the limit in a~multistage multiphase synthesis of substance
%J Sibirskij žurnal industrialʹnoj matematiki
%D 2012
%P 135-146
%V 15
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SJIM_2012_15_4_a13/
%G ru
%F SJIM_2012_15_4_a13
D. N. Shtokalo. On passage to the limit in a~multistage multiphase synthesis of substance. Sibirskij žurnal industrialʹnoj matematiki, Tome 15 (2012) no. 4, pp. 135-146. http://geodesic.mathdoc.fr/item/SJIM_2012_15_4_a13/